Question

Let $P\left(a_1,b_1\right)$ and $Q\left(a_2,b_2\right)$ be two distinct points on a circle with center $C(\sqrt{2},\sqrt{3})$. Let $O$ be the origin and $OC$ be perpendicular to both $CP$ and $CQ$. If the area of the triangle $OCP$ is $\frac{\sqrt{35}}{2}$, then $a_1^2+a_2^2+b_1^2+b_2^2$ is equal to ______

Answer 1

Answer: 24

$\frac{1}{2}\times PC\times \sqrt{5}=\frac{\sqrt{35}}{2};PC=\sqrt{7}$

$a_1^2+b_1^2+a_2^2+b_2^2=O{P}^2+O{Q}^2$
$=2(5+7)=24$